ترغب بنشر مسار تعليمي؟ اضغط هنا

The Integrals of Motion for the Deformed Virasoro Algebra

68   0   0.0 ( 0 )
 نشر من قبل Takeo Kojima
 تاريخ النشر 2007
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

We explicitly construct two classes of infinitly many commutative operators in terms of the deformed Virasoro algebra. We call one of them local integrals and the other nonlocal one, since they can be regarded as elliptic deformations of the local and nonlocal integrals of motion obtained by V.Bazhanov, S.Lukyanov and Al.Zamolodchikov.

قيم البحث

اقرأ أيضاً

n-ary algebras have played important roles in mathematics and mathematical physics. The purpose of this paper is to construct a deformation of Virasoro-Witt n-algebra based on an oscillator realization with two independent parameters (p, q) and investigate its n-Lie subalgebra.
60 - T. Kojima , J. Shiraishi 2007
We explicitly construct two classes of infinitly many commutative operators in terms of the deformed W-algebra $W_{qt}(sl_N^)$, and give proofs of the commutation relations of these operators. We call one of them local integrals of motion and the oth er nonlocal one, since they can be regarded as elliptic deformation of local and nonlocal integrals of motion for the $W_N$ algebra.
165 - P. Bouwknegt , K. Pilch 1997
We discuss some aspects of the representation theory of the deformed Virasoro algebra $virpq$. In particular, we give a proof of the formula for the Kac determinant and then determine the center of $virpq$ for $q$ a primitive N-th root of unity. We d erive explicit expressions for the generators of the center in the limit $t=qp^{-1}to infty$ and elucidate the connection to the Hall-Littlewood symmetric functions. Furthermore, we argue that for $q=sqrtN{1}$ the algebra describes `Gentile statistics of order $N-1$, i.e., a situation in which at most $N-1$ particles can occupy the same state.
55 - Shuai Guo , Gehao Wang 2016
The Hodge tau-function is a generating function for the linear Hodge integrals. It is also a tau-function of the KP hierarchy. In this paper, we first present the Virasoro constraints for the Hodge tau-function in the explicit form of the Virasoro eq uations. The expression of our Virasoro constraints is simply a linear combination of the Virasoro operators, where the coefficients are restored from a power series for the Lambert W function. Then, using this result, we deduce a simple version of the Virasoro constraints for the linear Hodge partition function, where the coefficients are restored from the Gamma function. Finally, we establish the equivalence relation between the Virasoro constraints and polynomial recursion formula for the linear Hodge integrals.
245 - Xiufu Zhang , Shaobin Tan 2009
In this paper, Whittaker modules for the Schrodinger-Virasoro algebra $mathfrak{sv}$ are defined. The Whittaker vectors and the irreducibility of the Whittaker modules are studied. $mathfrak{sv}$ has a triangular decomposition according to the Cartan algebra $mathfrak{h}:$ $$mathfrak{sv}=mathfrak{sv}^{-}oplusmathfrak{h}oplusmathfrak{sv}^{+}.$$ For any Lie algebra homomorphism $psi:mathfrak{sv}^{+}tomathbb{C}$, we can define Whittaker modules of type $psi.$ When $psi$ is nonsingular, the Whittaker vectors, the irreducibility and the classification of Whittaker modules are completely determined. When $psi$ is singular, by constructing some special Whittaker vectors, we find that the Whittaker modules are all reducible. Moreover, we get some more precise results for special $psi$.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا